Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x-3y &= 9 \\ -6x+2y &= -7\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-6x = -2y-7$ Divide both sides by $-6$ to isolate $x$ $x = {\dfrac{1}{3}y + \dfrac{7}{6}}$ Substitute this expression for $x$ in the first equation. $6({\dfrac{1}{3}y + \dfrac{7}{6}}) - 3y = 9$ $2y + 7 - 3y = 9$ Simplify by combining terms, then solve for $y$ $-1y + 7 = 9$ $-1y = 2$ $y = -2$ Substitute $-2$ for $y$ in the top equation. $6x-3( -2) = 9$ $6x+6 = 9$ $6x = 3$ $x = \dfrac{1}{2}$ The solution is $\enspace x = \dfrac{1}{2}, \enspace y = -2$.